In this article, the microscale ice crystal growth behavior under electrostatic field is investigated via a phase field method, which also incorporates the effects of anisotropy and thermal noise. The multiple ice nuclei’s competitive growth as disclosed in existing experiments is thus successfully predicted. The present approach suggests a highly efficient theoretical tool for probing into the freeze injury mechanisms of biological material due to ice formation during cryosurgery or cryopreservation process when external electric field was involved.

1.
Bischof
,
J. C.
, 2000, “
Quantitative Measurement and Prediction of Biophysical Response During Freezing in Tissues
,”
Annu. Rev. Biomed. Eng.
1523-9829,
2
, pp.
257
288
.
2.
Mazur
,
P.
,
Leibo
,
S. P.
, and
Chu
,
E. H.
, 1972, “
A Two-Factor Hypothesis of Freezing Injury. Evidence From Chinese Hamster Tissue-Culture Cells
,”
Exp. Cell Res.
0014-4827,
71
(
2
), pp.
345
55
.
3.
Mazur
,
P.
,
Seki
,
S.
,
Pinn
,
I. L.
,
Kleinhans
,
F. W.
, and
Edashige
,
K.
, 2005, “
Extra- and Intracellular Ice Formation in Mouse Oocytes
,”
Cryobiology
0011-2240,
51
(
1
), pp.
29
53
.
4.
Tao
,
L. R.
, and
Hua
,
T. C.
, 2000, “
An Experimental Study of Ice Formation in High Voltage Electric Field
,”
Heat Transfer Science and Technology
,
B. X.
Wang
, ed.,
Higher Education Publishing House
,
Beijing
, pp.
169
174
.
5.
Petersen
,
A.
,
Schneider
,
H.
,
Rau
,
G.
, and
Glasmacher
,
B.
, 2006, “
A New Approach for Freezing of Aqueous Solutions Under Active Control of the Nucleation Temperature
,”
Cryobiology
0011-2240,
53
(
2
), pp.
248
257
.
6.
Sun
,
W.
,
Xu
,
X.
,
Zhang
,
H.
, and
Xu
,
C.
, 2008, “
Effects of Dipole Polarization of Water Molecules on Ice Formation Under an Electrostatic Field
,”
Cryobiology
0011-2240,
56
(
1
), pp.
93
99
.
7.
Mao
,
L.
,
Udaykumar
,
H. S.
, and
Karlsson
,
J. O. M.
, 2003, “
Simulation of Micro-Scale Interaction Between Ice and Biological Cells
,”
Int. J. Heat Mass Transfer
0017-9310,
46
(
26
), pp.
5123
5136
.
8.
Chang
,
A.
,
Dantzig
,
J. A.
,
Darr
,
B. T.
, and
Hubel
,
A.
, 2007, “
Modeling the Interaction of Biological Cells With a Solidifying Interface
,”
J. Comput. Phys.
0021-9991,
226
(
2
), pp.
1808
1829
.
9.
Boettinger
,
W. J.
,
Warren
,
J. A.
,
Beckermann
,
C.
, and
Karma
,
A.
, 2002, “
Phase-Field Simulation of Solidification
,”
Annu. Rev. Mater. Res.
1531-7331,
32
, pp.
163
194
.
10.
Gránásy
,
L.
,
Pusztai
,
T.
,
Warren
,
J. A.
,
Douglas
,
J. F.
,
Börzsonyi
,
T.
, and
Ferreiro
,
V.
, 2003, “
Growth of ‘Dizzy Dendrites’ in a Random Field of Foreign Particles
,”
Nature Mater.
1476-1122,
2
(
2
), pp.
92
96
.
11.
Li
,
F. F.
,
Liu
,
J.
, and
Yue
,
K.
, 2008, “
Numerical Simulation on Ice Crystal Formulation in Cellular Level Based on Phase Field Theory
,”
Chin. J. Low Temp. Phys.
1000-3258,
30
(
2
), pp.
84
92
.
12.
Xu
,
Y.
,
McDonough
,
J. M.
,
Tagavi
,
K. A.
, and
Gao
,
D. Y.
, 2004, “
Two-Dimensional Phase-Field Model Applied to Freezing Into Supercooled Melt
,”
Cell Preservation Technology
,
2
(
2
), pp.
113
124
. 1538-344X
13.
Svishchev
,
I. M.
, and
Kusalik
,
P. G.
, 1994, “
Crystallization of Liquid Water in a Molecular Dynamics Simulation
,”
Phys. Rev. Lett.
0031-9007,
73
(
7
), pp.
975
978
.
14.
Braslavsky
,
I.
, and
Lipson
,
S. G.
, 1998, “
Electrofreezing Effect and Nucleation of Ice Crystals in Free Growth Experiments
,”
Appl. Phys. Lett.
0003-6951,
72
(
2
), pp.
264
266
.
15.
Wang
,
S. L.
,
Sekerka
,
R. F.
,
Wheeler
,
A. A.
,
Murray
,
B. T.
,
Coriell
,
S. R.
,
Braun
,
R. J.
, and
Mcfadden
,
G. B.
, 1993, “
Thermodynamically-Consistent Phase-Field Models for Solidification
,”
Physica D
0167-2789,
69
(
1–2
), pp.
189
200
.
16.
Karma
,
A.
, and
Rappel
,
W. J.
, 1999, “
Phase-Field Model of Dendritic Sidebranching With Thermal Noise
,”
Phys. Rev. E
1063-651X,
60
(
4
), pp.
3614
3625
.
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